Quantum Computing, Metrology, and Imaging

Information science is entering into a new era in which certain subtleties of quantum mechanics enables large enhancements in computational efficiency and communication security. Naturally, precise control of quantum systems required for the implementation of quantum information processing protocols implies potential breakthoughs in other sciences and technologies. We discuss recent developments in quantum control in optical systems and their applications in metrology and imaging.Comment: 11 pages, 6 figures; Proceedings of SPIE: Fluctuations and Noise in Photonics and Quantum Optics III (2005

High-fidelity linear optical quantum computing with polarization encoding

We show that the KLM scheme [Knill, Laflamme and Milburn, Nature {\bf 409}, 46] can be implemented using polarization encoding, thus reducing the number of path modes required by half. One of the main advantages of this new implementation is that it naturally incorporates a loss detection mechanism that makes the probability of a gate introducing a non-detected error, when non-ideal detectors are considered, dependent only on the detector dark-count rate and independent of its efficiency. Since very low dark-count rate detectors are currently available, a high-fidelity gate (probability of error of order $10^{-6}$ conditional on the gate being successful) can be implemented using polarization encoding. The detector efficiency determines the overall success probability of the gate but does not affect its fidelity. This can be applied to the efficient construction of optical cluster states with very high fidelity for quantum computing.Comment: 12 pages, 7 figures. Improved construction of high-fidelity entangled ancilla; references adde

Inefficiency of classically simulating linear optical quantum computing with Fock-state inputs

Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [Aaronson and Arkhipov, Theory Comput. 9, 143 (2013)]. Here we present an elementary argument that utilizes only techniques from quantum optics. We explicitly construct the Hilbert space for such an interferometer and show that its dimension scales exponentially with all the physical resources. We also show in a simple example just how the Schr\"odinger and Heisenberg pictures of quantum theory, while mathematically equivalent, are not in general computationally equivalent. Finally, we conclude our argument by comparing the symmetry requirements of multiparticle bosonic to fermionic interferometers and, using simple physical reasoning, connect the nonsimulatability of the bosonic device to the complexity of computing the permanent of a large matrix.Comment: 7 pages, 1 figure Published in PRA Phys. Rev. A 89, 022328 (2014

Alternate Scheme for Optical Cluster-State Generation without Number-Resolving Photon Detectors

We design a controlled-phase gate for linear optical quantum computing by using photodetectors that cannot resolve photon number. An intrinsic error-correction circuit corrects errors introduced by the detectors. Our controlled-phase gate has a 1/4 success probability. Recent development in cluster-state quantum computing has shown that a two-qubit gate with non-zero success probability can build an arbitrarily large cluster state with only polynomial overhead. Hence, it is possible to generate optical cluster states without number-resolving detectors and with polynomial overhead.Comment: 10 pages, 4 figures, 4 tables; made significant revisions and changed forma

Super-Resolving Quantum Radar: Coherent-State Sources with Homodyne Detection Suffice to Beat the Diffraction Limit

There has been much recent interest in quantum metrology for applications to sub-Raleigh ranging and remote sensing such as in quantum radar. For quantum radar, atmospheric absorption and diffraction rapidly degrades any actively transmitted quantum states of light, such as N00N states, so that for this high-loss regime the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the linear Beer's law for classical radar attenuation, and which provide sensitivity at the shot-noise limit in the returned power. We show that coherent radar radiation sources, coupled with a quantum homodyne detection scheme, provide both longitudinal and angular super-resolution much below the Rayleigh diffraction limit, with sensitivity at shot-noise in terms of the detected photon power. Our approach provides a template for the development of a complete super-resolving quantum radar system with currently available technology.Comment: 23 pages, content is identical to published versio

On the connection between quantum nonlocality and phase sensitivity of two-mode entangled Fock state superpositions

In two-mode interferometry, for a given total photon number $N$, entangled Fock state superpositions of the form $(|N-m\rangle_a|m\rangle_b+e^{i (N-2m)\phi}|m\rangle_a|N-m\rangle_b)/\sqrt{2}$ have been considered for phase estimation. Indeed all such states are maximally mode-entangled and violate a Clauser-Horne-Shimony-Holt (CHSH) inequality. However, they differ in their optimal phase estimation capabilities as given by their quantum Fisher informations. The quantum Fisher information is the largest for the $N00N$ state $(|N\rangle_a|0\rangle_b+e^{i N\phi}|0\rangle_a|N\rangle_b)/\sqrt{2}$ and decreases for the other states with decreasing photon number difference between the two modes. We ask the question whether for any particular Clauser-Horne (CH) (or CHSH) inequality, the maximal values of the CH (or the CHSH) functional for the states of the above type follow the same trend as their quantum Fisher informations, while also violating the classical bound whenever the states are capable of sub-shot-noise phase estimation, so that the violation can be used to quantify sub-shot-noise sensitivity. We explore CH and CHSH inequalities in a homodyne setup. Our results show that the amount of violation in those nonlocality tests may not be used to quantify sub-shot-noise sensitivity of the above states.Comment: Published online in Quantum Information Processin